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GCSE Physics Revision

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GCSE Physics revision

Conservation of momentum

Momentum (HT only)

AQA 4.5.7.2
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AQA student objectives

Learning pathway

All ยท Most ยท Some

ALL ๐ŸŽฏ

Use momentum as a model to describe, explain and calculate events such as collisions between objects.

MOST ๐ŸŽฏ๐ŸŽฏ

Apply conservation of momentum knowledge to a relevant numerical or graphical problem and show the working.

SOME ๐ŸŽฏ๐ŸŽฏ๐ŸŽฏ

Analyse an unfamiliar problem involving conservation of momentum and justify the method or conclusion.

Revision summary

Key knowledge

Read on screen, then print for Cornell-style active revision.

What is Momentum?

  • Momentum is a property of all moving objects, defined as the product of an object's mass and its velocity: p = mv .
  • The SI unit of momentum is kg m/s, combining the units of mass (kg) and velocity (m/s).
  • The symbol for momentum is p (the Greek letter rho, which looks like a 'p'), so the equation is written as p = mv .

Momentum as a Vector Quantity

  • Momentum is a vector quantity, meaning it has both a magnitude and a direction.
  • A chosen positive direction must be defined (e.g. rightwards = positive), and any object moving in the opposite direction is assigned a negative momentum.
  • For example, a dinosaur moving right has positive momentum, whilst a car moving left has negative momentum.

Calculating Momentum: Worked Examples

  • A 4,500 kg dinosaur charging at 12 m/s has a momentum of 4500 ร— 12 = 54,000 kg m/s.
  • A 1,200 kg car travelling at 25 m/s in the opposite direction has a momentum of โˆ’(1200 ร— 25) = โˆ’30,000 kg m/s.

The Principle of Conservation of Momentum

  • In a closed system, the total momentum before an event (such as a collision) is equal to the total momentum after the event.
  • A closed system is one where no external forces act, so no momentum is lost or gained during the event.
  • This principle applies to all collisions and explosions studied at GCSE level.

Applying Conservation of Momentum: Collisions

  • The total momentum before a collision is found by adding the individual momenta:
  • 54,000 + (โˆ’30,000) = +24,000 kg m/s.
  • After the collision, if the two objects move together, they are treated as a single combined mass of 4500 + 1200 = 5700 kg.
  • The shared velocity after the collision is found by rearranging p = mv to give v = mp = 24,000
  • 5700 โ‰ˆ 4.2 m/s to the right.
  • A positive result confirms the combined objects move in the direction of the object that had greater momentum.

Conservation of Momentum When Initial Momentum is Zero

  • If a system is initially stationary, its total momentum is zero, so the total momentum after any event must also equal zero.
  • This means that if one part of the system gains momentum in one direction, another part must gain an equal momentum in the opposite direction.
  • A gun firing a bullet is a classic example: the bullet gains forward momentum, so the gun recoils backwards with an equal and opposite momentum.

Worked Example: Gun Recoil

  • A 0.005 kg bullet fired at 120 m/s has a momentum of 0.005 ร— 120 = 0.6 kg m/s.
  • Since total momentum must remain zero, the gun's momentum must be โˆ’0.6 kg m/s.
  • Using v = m = โˆ’0.6 p
  • 2
  • = โˆ’0.3 m/s, the gun recoils at 0.3 m/s in the opposite direction to the bullet.

Key Momentum Equation Summary

  • The momentum equation p = mv links momentum (p, in kg m/s), mass (m, in kg), and velocity (v , in m/s).
  • p p
  • The equation can be rearranged to find mass m = v or velocity v = m depending on the unknown quantity.
  • Always assign a positive or negative sign to velocities and momenta based on the chosen direction before substituting values.

Common Exam Tips for Momentum

  • Always state the direction of momentum in your answer, as it is a vector quantity.
  • Remember to convert units where necessary, for example grams to kilograms, before substituting into p = mv .
  • When two objects collide and stick together, add their masses to find the combined mass for use in the post-collision calculation.

Conservation of Momentum

  • The law of conservation of momentum states that the total momentum before an event equals the total momentum after an event.
  • Conservation of momentum only applies in a closed system, where no external forces such as friction or air resistance are acting.
  • Because momentum is a vector, momenta in opposite directions can cancel out, allowing the total to remain zero.

Explosion-Type Situations (Zero Initial Momentum)

  • When an object is initially stationary, its total momentum is zero, so the total momentum after the event must also be zero.
  • An example is a skateboarder falling: the skateboard moves right (positive momentum) and the person moves left (negative momentum), so they cancel to give zero total momentum.
  • Another example is a gun recoiling: the bullet travels forward with positive momentum and the gun recoils backwards with equal negative momentum, keeping the total at zero.

Collisions Where Objects Stick Together

  • When two objects collide and stick together, their masses must be added together (m_1 + m_2) and treated as a single object after the collision.
  • The momentum before the collision equals the momentum after: m_1 v_1 = (m_1 + m_2) v_2, where v_2 is the shared velocity afterwards.
  • Because the combined mass is greater after the collision, the velocity must decrease to conserve the same total momentum.

Head-On Collisions Where Objects Stop

  • When two objects travel towards each other and stop, their total momentum before must equal zero, since the final momentum is zero.
  • To show this, assign one object a positive momentum and the other a negative momentum (as they travel in opposite directions), and demonstrate they sum to zero.
  • This situation is essentially the reverse of an explosion, where zero total momentum is maintained throughout.

Complex Collisions with Rebound

  • In collisions where objects rebound and both have separate velocities afterwards, use the equation: total momentum before = total momentum after.
  • It is essential to carefully assign positive and negative signs to each object's velocity based on its direction of travel.
  • Write out all known values, substitute them into the momentum equation, and use algebra to find the unknown quantity.

Force and Rate of Change of Momentum

  • The equation linking force and momentum is F = ฮ”(mv) / ฮ” t, meaning force equals the rate of change of momentum.
  • This equation shows that force and time are inversely proportional: increasing the time of impact reduces the force experienced.
  • Reducing the force also means reducing the rate of change of momentum, which is the key phrase to use in exam answers.
  • Alternatively, reducing the force can be described as reducing the acceleration, consistent with Newton's Second Law (F = ma).

Safety Applications of Momentum

  • Devices such as airbags, crumple zones, crash barriers, and soft surfaces all work by increasing the time taken for an impact to occur.
  • By increasing the impact time, the rate of change of momentum is reduced, which in turn reduces the force on the person or object.
  • A full exam answer on safety should mention: increasing the time of impact, reducing the rate of change of momentum, and reducing the force (or acceleration).

Momentum Calculation Tips for Separate Science

  • For separate science GCSE, you must be able to carry out numerical momentum calculations across all four types of situation.
  • Always check the direction of motion and assign consistent positive and negative signs before substituting values into equations.
  • If objects stick together after a collision, remember to add their masses before calculating the final velocity using v = p / m_1 + m_2.
  • If asked to find the velocity of a recoiling object (e.g. a gun), rearrange the conservation equation so that the two momenta sum to zero and solve for the unknown.